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jekas [21]
3 years ago
13

Answer in Standard form!

Mathematics
2 answers:
Vlad1618 [11]3 years ago
8 0
The question please or a photo?
myrzilka [38]3 years ago
3 0
Whats the the question i can't write it in standard form if i have nothing to write 
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Find a formula for the sum of the first n even positive integers.
melisa1 [442]
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
{k}^{2}  + k
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
7 0
2 years ago
Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a
Bond [772]

f(x)=3\sin x+3\cos x\implies f'(x)=3\cos x-3\sin x

f has critical points where f'=0:

3\cos x-3\sin x=0\implies\cos x=\sin x\implies\tan x=1\implies x=\pm\dfrac\pi4+2n\pi

where n is any integer. We get solutions in the interval \left[0,\frac\pi3\right] for n=0, for which x=\frac\pi4.

At this critical point, we have f\left(\frac\pi4\right)=3\sqrt2\approx4.243.

At the endpoints of the given interval, we have f(0)=3 and f\left(\frac\pi3\right)=\frac{3+3\sqrt3}2\approx4.098.

So we have the extreme values

\max\limits_{x\in\left[0,\frac\pi3\right]}f=3\sqrt2

\min\limits_{x\in\left[0,\frac\pi3\right]}f=3

8 0
3 years ago
Evaluate the expression 4+−4√2+−1√ and write the result in the form a+bi.
castortr0y [4]

In the expression, the real number a equals 12 and the real number b equals -16.

<h3>How to explain the information?</h3>

It should be noted that the expression given is:

= (4 - 2i)²

Therefore, we need to expand the expression. This will be:

= (4 - 2i)(4 - 2i)

= 16 -8i -8i + 4i²

= 16 -16i +4i²

Substitute -1 for i²

= 16 - 16i + 4(-1)

= 16 - 16i - 4

= 12 - 16i

Therefore, the value of the expression is 12 - 16i.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Evaluate the expression ( 4 − 2 i )² and write the result in the form a + b i.

8 0
2 years ago
Which number line models the expression -3 + 5 ?
damaskus [11]
I think the answer would be B
3 0
3 years ago
Ricardo is buying juice boxes for snack packs. Which is the best buy?
patriot [66]
Ummm I don’t find a way to give this a response, but the Best Buy it would be snack packs because he’s getting a finance
8 0
3 years ago
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